SCEC Workshop - October 2003

1. SCEC Workshop - October 2003 Practical considerations for the future from a structural engineering perspective Craig D. Comartin

2. Outline • Background on performance-based engineering • Financial formulation of PBE • Implications for practice • Some important needs

3. PEER framing equation Decision variable annualized loss performance objective Damage measure casualties capital loss downtime Engineering demandparameter displacement drift Intensity measure hazard curve level of shaking Pacific Earthquake Engineering Research Center

4. Decision: Should this building be retrofitted? Yes, if it is unsafe for shaking with a 10% chance of being exceeded in 50 yrs. No, if it is safe for shaking with a 10% chance of being exceeded in 50 yrs.

5. Elements and Components Returns included in properties of components A1 and A5 A2 A3 A1 A5 A4 Wall element A Wall element B Components Global Structure Wall Element A

6. Component force-deformation tests deformation force

7. Component Behavior and Properties Backbone curve Force Actual hysteretic behavior Deformation Backbone curve from actual hysteretic behavior

8. Component Behavior and Properties Backbone Idealized component curve behavior C B, C, D B C, D B E D A A E A E Ductile Semi-ductile Brittle (force contolled) (deformation controlled) Idealized component behavior from backbone curves

9. Nonlinear dynamic analysis

10. Equivalent single degree of freedom

11. Global force-deformation relationship(Pushover or Capacity Curve) D Force Parameter, V V TOTAL Displacement Parameter, D

12. Global Displacement and Damage Immediate Life Collapse occupancy safety prevention Building Damage States Global Force Parameter Global capacity curve Global Displacement Limits, d c Performance Levels

13. Performance levels • Severe structural damage Collapse Prevention • Incipient Collapse Probable • Probable falling hazards total loss • Possible restricted egress • Probable structural damage Life Safety • No Collapse Possible • No falling hazards total loss • Adequate emergency egress Damage • Slight structural damage • Life safety attainable Control 2 to 3 • Essential systems repairable • Moderate overall damage weeks • Negligible structural damage Immediate Occupancy • Life safety maintained 24 • Essential systems operational hours • Minor overall damage Performance Level Damage State Down Time

14. Spectral representation Elastic spectrum

15. Nonlinear static analysis Elastic spectrum

16. Performance point Intensity measure Damage measure Global Force Parameter, V Building Damage States Performance Point Global capacity curve Immediate Life Collapse Global occupancy safety prevention Displacement m Inelastic spectrum methods (R, , T) Limits, d 3.0 c Performance Levels m=1 m=2 2.0 m=4 m=8 Strength Demand (g) 1.0 Engineering demand parameter 0.0 0.0 1.0 2.0 3.0 4.0 Period,T (sec.)

17. Decision: Should this building be retrofitted? No, if it is safe for shaking with a 10% chance of being exceeded in 50 yrs.

18. Decision: Should the structural system for this new building be upgraded? Yes, if the benefits of the upgrade exceed the additional costs.

19. Force Sa P(IM) 10-3 10-2 10-1 EDP (displacement) P(EDP) T Range of seismic intensity (IM) Pushover curve 1.0 10-1 10-2 EDP 10-3 10-4 EDP (displacement) hazard Engineering demand parameter and intensity measure

20. EDP to damage and loss Damage Force EDP (displacement) Loss Casualties Capital loss Business interruption EDP (displacement) Loss as a function of EDP Pushover curve

21. P(Loss) Integrate for expected annual loss 1.0 10-1 P(EDP) 10-2 Loss ($) 10-3 10-4 Loss Risk of Loss 1.0 10-1 EDP (displacement) 10-2 EDP 10-3 10-4 EDP (displacement) hazard Risk and expected annual loss Loss as a function of EDP

22. UC Berkeley – Stanley Hall Item Cost Capital $160 million Contents $50 million Business Interruption $40 million annually

23. UC Berkeley – Stanley Hall $139K reduction in expected annual losses for unbonded braces compared to conventional system Capital/Contents Business Interruption $400 $207 $300 ($,000) $200 $113 $100 $188 $143 $0 SCBF (conventional braces) UBB (unbonded braces)

24. UC Berkeley – Stanley Hall $0.1 $0.6 $1.1 $1.7 $2.1 $2.4 $2.5 Benefit $1.2 $1.2 $1.2 $1.2 $1.2 $1.2 $1.2 Cost Benefit–cost ratio (BCR) 2.5 2 5% discount 1.5 1 0.5 0 1 5 10 20 30 40 50 Building Life (years)

25. ATC 58 Performance-based Seismic Design Guidelines Joe’s Joe’s Joe’s Joe’s Joe’s Joe’s Joe’s Joe’s Joe’s Joe’s Joe’s Joe’s Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Beer! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Food! Operational Operational Immediate Life Life Collapse Collapse Occupancy Safety Safety Prevention Prevention Federal Emergency Management Agency FEMA - 349 • Multiple Volumes • Seismic Performance Prediction for Buildings • Performance-based Seismic Design • Recommended Prescriptive Criteria for Performance-based Seismic Designs Guidelines forPerformance-basedSeismic Design Joe’s Joe’s Joe’s Joe’s Beer! Beer! Beer! Beer! Beer! Beer! Food! Food! Food! Food! Food! Food!

26. Traditional traditional questions for structural engineer 1. What is your fee? 2. Does it meet “code”?

27. Future questions for structural engineers • What would be the losses at my facility? • What is the return on investment in retrofit? • Does it pay to upgrade criteria for new construction? • What is a fair premium for insurance? • How does my seismic risk compare with others I face?

28. FEMA 440: Improvement of inelastic seismic analysis procedures Equivalent Linearization Displacement Modification FEMA-356 Displacement Coefficient Method (DCM) ATC- 40 Capacity Spectrum Method (CSM)

29. Nonlinear response history evaluation database  20 NEHRP-B 20 NEHRP-C SDOF oscillators Ground motion records Maximum displacements (elastic plus inelastic) 20 NEHRP-D 20 NEHRP-E/F 20 NEAR-FAULT 50 periods of vibration (0.05s – 3.0s) Damping ratio x=5% 180,000 total 9 levels of relative strength R = 1 (elastic),1.5, 2, 3, 4, 5, 6, 7, 8 4 hysteretic behaviors (EPP, SD, SSD, NL)

30. Evaluation of improved procedures

31. Evaluation of improved procedures

32. Nonlinear dynamic analysis

33. Nonlinear static analysis Elastic spectrum

34. Equivalent single degree of freedom

35. Multi-degree-of-freedom (MDOF) effects Estimate response parameters made using simplified inelastic procedures. Compare with results obtained by nonlinear dynamic analysis from Aschheim 2002

36. Overturning Moments— Weak-story 9-story frame 200000 200000 2% Drift 4% Drift Overturning Moment (kips-ft) Overturning Moment (kips-ft) 150000 150000 100000 100000 50000 50000 0 0 Floor Floor 1st 1st 9th 8th 7th 6th 5th 4th 9th 8th 7th 6th 5th 4th 3rd 3rd 2nd 2nd Weak—2 % Weak—4 % from Aschheim 2002

37. Potential simplified NDP 200000 4% Drift Overturning Moment (kips-ft) 150000 100000 50000 0 Floor 9th 8th 7th 6th 5th 4th 1st 3rd 2nd • Do NSP analysis to estimate global displacement. • Select one (few?) response histories and scale to result in same global displacement. • Use results to evaluate MDOF effects.

38. Factors that may reduce response of short period buildings 1. Neglecting ascending branch of design spectra 2. Short, stiff buildings more sensitive to SSI 3. Radiation and material damping in supporting soils 4. Full and partial basements 5. Incoherent input to relatively large plan dimensions 6. Concentrating building masses at floor and roof levels

39. structural components of foundation geotechnical components of foundation Infinitely rigid foundation and soil ug= free field motion (FFM) with conventional damping ug= free field motion (FFM) with conventional damping a) Rigid base model b) Flexible base model ug= foundation input motion (FIM) with conventional damping ug= foundation input motion (FIM) with system damping including foundation damping Kinematic interaction (high T-pass filter) Adjust for foundation damping Kinematic interaction (high T-pass filter) free field motion (FFM) with conventional damping foundation input motion (FIM) with conventional damping free field motion (FFM) with conventional damping c) Kinematic interaction d) Foundation damping

40. Example building for SSI effects 160’-0” 100’-0” 8” R/C wall – 20’L typical Plan 20’-0” Roof 10’-0” typical 2nd 1st 3’D Footing 26’L x 3’B x 1.5’t Elevation @ wall Section @ wall

41. SSI example

42. Example building(displacement modification procedure) C C Procedure Cap Base SSI dy T Sa R d mu 0 1 Current yes fixed 0.1 0.14 1.5 3.8 1.2 1.5 0.5 5.0 yes flexible 0.2 0.21 1.5 3.8 1.2 1.4 1.1 5.4 no fixed 0.1 0.14 1.5 3.8 1.2 3.4 1.2 11.8 no flexible 0.2 0.21 1.5 3.8 1.2 2.4 1.8 9.2 Improved fixed no 0.1 0.14 1.5 3.8 1.2 2.6 0.9 8.8 fixed yes 0.1 0.14 0.8 2.0 1.2 1.6 0.3 2.9 flexible no 0.2 0.21 1.5 3.8 1.2 1.7 1.3 6.6 flexible yes 0.2 0.21 0.8 2.0 1.2 1.3 0.5 2.6

43. Effects of Foundations on Performance Foundation stiffness and strength affect D ,large Large various structural components differently. displacements cause frame High forces damage D cause shear , small wall damage Stiff and strong is not always favorable; nor is flexible and weak always conservative. Foundationyielding androcking protectsshear wall Smalldisplacements protect framefrom damage Stiff and Strong Foundation Flexible and Weak Foundation

44. Pier load tests Dynamic Static Conventional estimates based on unconfined compression strength